OULU BUSINESS SCHOOL

Chao Ding

THE ECONOMICS OF SOLAR PHOTOVOLTAICS AND ITS POTENTIAL IN FINLAND

Master’s Thesis

Department of Economics

Oulu Business School

December 2015

CONTENTS

1 INTRODUCTION............................................................................................... 5

2 TECHNOLOGICAL DEVELOPMENT OF PV AND CHALLENGES IN PV GENERATION ............................................................................................. 7

2.1 Overview of PV technologies ..................................................................... 7

2.1.1 Crystalline silicon ............................................................................. 8

2.1.2 Thin-film ........................................................................................... 9

2.1.3 Third-generation ............................................................................. 10

2.1.4 Development trend .......................................................................... 11

2.1.5 Global trend for PV deployment ..................................................... 12

2.2 Technical challenges of PV generation ................................................... 14

2.2.1 Variability ....................................................................................... 14

2.2.2 Intermittency ................................................................................... 15

3 SMART GRID AND PV ................................................................................... 17

4 SHORT-RUN ECONOMIC QUESTIONS .................................................... 20

4.1 Short-run costs ......................................................................................... 20

4.2 Short-run benefits .................................................................................... 24

4.3 Short-run net benefits .............................................................................. 27

5 LONG-RUN ECONOMIC QUESTIONS....................................................... 30

5.1 Integration costs ....................................................................................... 30

5.1.1 Redefining integration costs ........................................................... 30

5.1.2 Decomposing integration costs ....................................................... 33

5.2 The model of Gowrisankaran et al. (2013)............................................. 37

5.2.1 The model setting ............................................................................ 37

5.2.2 The stage-two optimization problem .............................................. 38

5.2.3 The stage-one optimization problem .............................................. 42

5.2.4 Summary of the findings from Gowrisankaran et al. (2013) .......... 43

6 CASE STUDIES ON SOLAR PV DEPLOYMENT ...................................... 45

6.1 PV deployment in Germany .................................................................... 45

6.2 Finland ...................................................................................................... 48

6.2.1 PV deployment in general ............................................................... 48

6.2.2 PV potential in Finland ................................................................... 49

6.2.3 Cost competitiveness of residential PV system .............................. 56

7 FUTURE OF PV ............................................................................................... 59

REFERENCES ......................................................................................................... 62

APPENDICES

Appendix 1 Monthly electricity output of 1 kWp PV system in Finnish cities

from South to North ................................................................................ 67

Appendix 2 Monthly electricity output of 1 kWp PV system in Finland and

other European cities .............................................................................. 69

Appendix 3 The optimum inclination angle for the solar panel installed in

different Finnish cities ............................................................................. 70

FIGURES

Figure 1. PV production development by technology 1980–2014 (Fraunhofer ISE 2015: 19).

Data: Navigant (2000-2010), IHS (Mono-/Multi- proportion by Paula Mints) (2011–2014). . 9

Figure 2 Cumulative installed PV power (MW) from 1992 to 2014 (International energy

agency photovoltaic power systems programme 2014, IEA PVPS 2015). .............................. 12

Figure 3 Annual installed PV power (MW) from 1992 to 2014 (International energy agency

photovoltaic power systems programme 2014, IEA PVPS 2015). ........................................... 13

Figure 4 The hierarchical structure of the existing grid (Farhangi 2010). ............................. 18

Figure 5 The smart grid (Moxa Inc 2013, reproduced with permission). .............................. 19

Figure 6 Integration costs evaluated from two perspectives Hirth et al. (2015). ................... 33

Figure 7 Find the optimal orientation for the solar PV system installed in Finland ............. 53

Figure 8 Solar PV potential heat map of Finland, map from (GADM 2015). ........................ 55

TABLES

Table 1 Empirical values of coefficients for c-Si, CIS and Cd-Te (Huld et al. 2010). ........... 51

Table 2 Efficiency coefficients for the inverter (Macedo & Zilles 2007). ............................... 52

Table 3 The LCOE estimates for different solar systems in Oulu .......................................... 58

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5

1 INTRODUCTION

Sun is the ultimate energy source in our planet. For nearly two centuries, the direct

conversion of sunlight into electricity (solar photovoltaics or solar PV for short), has

been understood to be a possibility. The inexhaustibility and ubiquity of the sun, the

unit-cost-free production and the low greenhouse gas (GHG) emission nature render

it advantages over other energy resources.

Still all the way until 2008, most countries had not mapped it into their energy mix

for electricity generation. This was primarily due to lack of cost competitiveness

opposite to the fossil fuels and uncertainty resulting from intermittency of

production. Up to now the conventional technologies still hold substantial cost

advantages over solar electricity generation when the social costs incurred by GHG

emissions are ignored. Also as Hirth, Ueckerdt and Edenhofer (2015) suggest, the

integration costs of solar PV are sizable at high penetration rate.

As concerns over the effects of GHG emissions mount, governments have begun

implementing policies favouring renewable energy sources like solar. In the

meantime, the prices of PV modules and systems have fallen dramatically. Reasons

behind this can be summarized as constant advancements in solar PV technology,

steep learning curve and the competition in solar manufacturing worldwide,

especially with the strong entrance of Chinese producers. Accordingly, a surge of

solar panel installations appeared and solar PV sales started an exponential growth in

2003. Globally the cumulative installed capacity of PV has leapt from a negligible

amount of 0.1 gigawatts in 1992 to over 150 gigawatts in early 2014 (International

energy agency 2010a, IEA 2014).

The rapid expansion of solar generation on different scales—utility, commercial and

residential—seems poised to go on for years. This trend can be seen from the growth

in desires of consumers, cities and regions to include solar energy into their energy

portfolio for hedging against price volatility of electricity generated by fossil fuels

(IEA 2011). The accelerated global warming necessitates its further widespread

deployment. There lies a great potential of solar energy along with other renewable

energy in the global energy market. Countries like the US, Germany and Japan keep

6

leading the global market in solar PV, while China and India with a late start, have

worked their ways to the top five of the solar PV technology-specific index ranking

(Renewable energy country attractiveness index 2015).

In this master’s thesis we begin with a brief introduction of solar PV technologies

and its integration with smart grid. Then we proceed to the economic questions of PV

in the short run and long run respectively. In the short run, only the net benefits of

marginal increases in solar PV capacity is considered while holding the existing grid

and technology constant. We introduce a primary metric, the levelized cost of

electricity (LCOE), to measure short-run costs of electricity generation. As for

short-run benefits, evaluation is based on a model extended by Baker, Fowlie,

Lemoine and Reynolds (2013). Long-run analyses are conducted by two different

approaches. One is decomposition of integration costs proposed by Hirth et al.

(2015) with integration costs accounting for the variability of renewables. The other

one, developed by Gowrisankaran, Reynolds and Samano (2013), starts with a

system operator’s two-stage welfare-maximizing problems and solves for the optimal

values of investment level of fossil fuel generators and interruptible power contract

price at different penetration rate of solar. The economic value of solar energy is then

calculated under such optimal conditions.

After the discussions of short-run and long-run economic questions, we bring up two

cases of solar PV from Germany and Finland respectively in section 6. The policy

options used in German history to encourage solar PV deployment are briefly

presented. As solar PV is comparatively new for the Finnish market and its

deployment is still at a low level nationwide, we give more treatment to the Finnish

case. Moreover, we look into the potential of solar PV in Finland especially with the

assistance of a comprehensive climatological database Meteonorm. The annual

energy output of a 1 kWp solar PV system inclined to the optimum angle in 30

Finnish cities is calculated in the mathematical frameworks of Huld, Beyer and Topič

(2010) and Macedo and Zilles (2007). The last but not the least, we report the LCOE

values of three different solar systems in Oulu. This thesis wraps up with the

discussion of PV’s future.

7

2 TECHNOLOGICAL DEVELOPMENT OF PV AND CHALLENGES IN

PV GENERATION

The term “photovoltaic” is a compound word consisting of “photo” with the meaning

of “light” in Greek and “volt”, the SI unit of electro-motive force. Semantically, solar

PV technology is a technology using solar cells layered with semi-conducting

material to convert sunlight (photons) directly into electricity (voltage). The solar

cell functions as a middleman on which the sunlight creates an electric field, which

in turn generates direct current electricity flows.

A typical solar PV system includes a solar panel and other parts known as the

Balance-of-system (BOS). A solar panel is then composed of an array of modules

which is formed by cells. An off-grid PV system generally consists of modules,

possible inverters for the transformation of direct current to alternate current,

possible batteries for storage of spare electricity and mounting frames. An on-grid

PV system does not require batteries and contains in addition to an off-grid system

other parts of BOS, for instance, transformers, electrical protection devices, wiring,

monitoring equipment and sun-tracking systems if any (IEA 2011). Moreover other

than physical appliances, labour, permitting, shipping, overheads, instalment cost and

land could also be incorporated in a broader range of BOS (Baker et al. 2013). In the

most general sense, BOS encompasses all non-module costs of a PV system.

2.1 Overview of PV technologies

At present, two families of PV technologies commonly applied for the cell

manufacturing are available for commercial use, namely crystalline silicon (c-Si) and

thin-film technology. Concentrating photovoltaics (CPV) is recently developed for

utility-scale electricity generation. Third-generation technologies still under

development are expected to strongly challenge their predecessors. For comparison

among technologies, the cell and/or module efficiency is an essential criterion. The

efficiency measures the conversion rate of solar energy striking the cell converted

into electricity, but in a rather standard context. Standard test conditions (STC)

specify a cell or module temperature of 25 ± 2 °C and an irradiance of 1000 W/ m2

with an air mass of 1.5 (Florida solar energy center 2010).

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2.1.1 Crystalline silicon

So far, wafer-based crystalline silicon (c-Si) is the most widely used technology

holding around 92% of the global market in 2014 (Fraunhofer Institute for Solar

Energy Systems ISE 2015). The reason behind this market domination is explained

by high solar cell efficiency, long-term stability and abundance of the raw material

needed for c-Si technology.

The material used in c-Si technology is silicon. Based on the form of sliced silicon,

crystalline silicon can be further divided into three main categories. The adoption of

highly purified silicon ingots is for monocrystalline (mono-Si) technology, silicon

castings for polycrystalline or multicrystalline (multi-Si), and grown ribbon of silicon

for ribbon sheets (ribbon-Si).

Among others technologies, monocrystalline has the highest efficiency ranging from

14% to 22%. Multicrystalline falls behind it with an efficiency of 12% to 19%. (IEA

2011.) Multi-Si uses less-purified silicon and is therefore cheaper to produce. The

tradeoff is therefore between cost and efficiency. The current trend for c-Si

technology adoption is moving toward multi-Si. Figure 1 depicts this trend with the

dark blue band marking multi c-Si’s annual share in global production from 1980 to

2014. A clear growth path of multi-Si can be observed. As for Ribbon-Si

technology, it captured only a negligible share of the market before 2011 and has

been driven out of the competition since 2011.

9

Figure 1. PV production development by technology 1980–2014 (Fraunhofer ISE 2015: 19).

Data: Navigant (2000-2010), IHS (Mono-/Multi- proportion by Paula Mints) (2011–2014).

Graph: PSE AG (2015).

2.1.2 Thin-film

Thin-film technologies are developed to address the technical challenge of high cost

in the production process of highly purified silicon. The solar cells from this

technology are very thin with an extremely thin layer of semiconductors deposited

onto an inexpensive backing such as glass, stainless steel or plastic. The direct

outcome of decreasing material use and applying high automation in production,

namely roll-to-roll printing, is a drop in costs.

However, its cost advantage is overshadowed by the poor performance of the cell.

Compared to c-Si technology, thin-film demonstrates a lower level of efficiency. For

each of the three primary thin-film technologies, the cell efficiency falls into the

range of 4% to 8% (amorphous silicon), 11% (cadmium telluride) and 7% to 12%

(copper indium selenide and copper indium gallium selenide) (IEA 2011). Even

though the latter two thin-film technologies have higher cell efficiencies, there are

environmental concerns over cadmium’s toxicity and a scarcity issue with telluride

and indium. These factors are seen as impediments for cadmium telluride (Cd-Te),

copper indium selenide (CIS) and copper indium gallium selenide (CIGS) to be

broadly adopted. Nevertheless, there is no unanimous attitude among countries and

other interest groups over the toxicity of CdTe technology.

10

The worldwide trend for annual thin-film production is thus complicated. Figure 1

shows its rapid market penetration starting from 1980 which peaked at over 30% in

1988. Then the production slowed down constantly in the following years. Only after

2005 the production resumed to grow and stabilized at around 10% of global market.

2.1.3 Third-generation

The great potential of solar PV in future energy market has motivated researchers to

develop new PV technologies. There are several emerging technologies, often

referred as third-generation technologies, worth to mention. They are either about to

be commercialized or still in the research stage.

Organic PV (OPV) cells replace silicon by organic polymers or small molecules with

semiconducting properties as the input material for electricity generation. The

recorded laboratory cell efficiency is as low as 4–5% (Tyagi, Rahim, Rahim and

Selvaraj 2012). Other main drawback of OPV is susceptibility to chemical

degradation from oxygen and water and also interfacial degradation from sunlight or

heat. Despite its low efficiency and instability, OPV cells have a high

cost-effectiveness, which compensates much of the aforementioned disadvantages.

Dye-sensitized solar cell, a hybrid cell between organic and inorganic, differs from

the conventional cell in a way that light-absorptive dye is separated from the charge

carrier transport. This mechanical design enables dye-sensitized cells to permit

impurity of both materials and cell’s operational environment. On the other hand, the

impurity can cause a dramatic shortening of cells’ lifetime. In addition, the use of

liquid electrolyte poses a big challenge of temperature stability to dye-sensitized

solar cells, though replacement of liquid electrolyte with a gel electrolyte often

solves this problem. (Goetzberger, Hebling and Schock 2002.) The laboratory

efficiency of dye-sensitized solar cell is on an order of 11.1% (Margolis, Coggeshall

and Zuboy 2012).

Multi-junction cells stack several cells with different bandgaps in a descending order

to maximize absorbance of the solar spectrum. Compared to conventional

single-junction cells, they capture more energy from the sun and naturally achieve

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high cell efficiency of over 40% in the lab. Multi-junction cells are more applicable

to concentrating photovoltaics and space applications due to their high expenses and

complex manufacturing process resulted from installation of sun-tracking systems.

(Friedman 2010.)

Quantum dots are nanocrystals with electronic properties which resemble those of

bulk semiconductors and discrete molecules. They have potential for high cell

efficiency through multiple exciton generation for each photon received. Currently,

quantum dots technology is still under research with low scoring of laboratory cell

efficiency, though the theoretical maximum efficiency is more than 40% (IEA 2011).

In future, quantum dots can compete against multi-junction cells with their cost

advantages.

2.1.4 Development trend

Based on different price-performance ratios of different PV technologies the vision

for their division in future PV market seems clear. With an overwhelmingly

dominating power, c-Si is bound to still prosper for a long time while other existing

PV technologies undergo constant improvements and new technologies continuously

developed to challenge it. Despite the relative maturity of c-Si technology, there is

room in it for future research and cost reduction by cutting the thickness of solar

cells, which directly lessens the use of highly purified silicon. Justified expectation

is a mix of PV technologies, since no technology appears strictly better than others

when both cost reduction and cell efficiency are taken into consideration.

The challenge posed to any PV technology is how to calibrate the tension between

cost reduction and conversion efficiency of solar cells for a desirably low

price-performance ratio. When evaluating the cost and efficiency for a given PV

technology, the indirect benefit from high conversion efficiency, a low demand of

land for panel use and thus small spending on land, should also be considered (Baker

et al. 2013). For organic cells, there is an additional need for improvement in cells’

lifetime. A longer lifetime cuts replacement costs and mitigates the uncertainty over

cell instability.

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2.1.5 Global trend for PV deployment

As solar photovoltaic technologies mature over time, the world has witnessed a

growing trend of adoptions in solar photovoltaic. The global PV capacity has

expanded from around 44.2 megawatts (MW) in 1992 to no less than 177 gigawatts

(GW) in 2014 at a compound annual growth rate of 43.4 % during the period. The

solar electricity generation alone meets at least 1% of global electricity demand in

2014. For the period of 1996 to 2014 the annual installed PV has exhibited an

exponential growth with a starting value of 26.6 MW and an ending value of 38.7

GW. Figure 2 and 3 below provide additional illustrations of the deployment trend

around the world. (International energy agency photovoltaic power systems

programme 2014, IEA PVPS 2015.)

44,2

177000

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Cumulative installed PV power (MW)from 1992 to 2014

Figure 2 Cumulative installed PV power (MW) from 1992 to 2014 (International energy agency

photovoltaic power systems programme 2014, IEA PVPS 2015).

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44,2

39957,3 38700

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10000

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Annual installed PV power (MW)from 1992 to 2014

Figure 3 Annual installed PV power (MW) from 1992 to 2014 (International energy agency

photovoltaic power systems programme 2014, IEA PVPS 2015).

For a large part of it, the global boom in PV deployment can be explained by large

price drops in PV module industry. This cost behaviour phenomena are known as the

experience curve effects which are the products of economies of scale and

technological improvements. Based on the most recent photovoltaic report of

Fraunhofer ISE (2015), every doubling in cumulative production of PV modules in

the last 34 years was followed by a price drop of 19.6% which is also known as the

learning rate. Historically the learning rate for PV modules had stayed as high as

22.8% on average over the period 1976–2003 (IEA 2011).

14

Figure 4. Price experience curve for PV module 1980–2014 (Fraunhofer ISE 2015: 40).

Data: Strategies Unlimited, Navigant Consulting, EUPD and pvXchang (1980–2010),

HIS (2011–2014).

Graph: PSE AG (2015).

2.2 Technical challenges of PV generation

In addition to the aforementioned challenges of PV technology, the technical

challenges of PV generation arise from the non-dispatchability, which in many ways

weakens the attractiveness of PV deployment compared to the conventional sources.

Solar electricity cannot always be dispatched when desired and its generation solely

depends on the sunshine that is unaffected by human interruptions. The unique

characteristics of the sunshine define the variability and intermittency of solar

electricity generation. (Baker et al. 2013.)

2.2.1 Variability

The sunshine which reaches earth is not constant and varies both quantitatively and

qualitatively. Its availability and intensity decide the amount of electricity that can be

15

harvested. Consequently, the amount of electricity produced by photovoltaic

fluctuates over the natural cycles of solar irradiation. Due to the diurnal and seasonal

patterns in the irradiation, the solar PV generation reaches its peak at midday and in

summer with the exceptional production in the equator area, where theoretically PV

generation level remains constant throughout the year. (Gul & Stenzel 2005.)

Variability in the solar context can be interpreted in two ways: altering production

levels in solar PV over time resulting from instability as well as diurnal and seasonal

variations which are predictable shifts in PV generation. Instability is not a problem

but an advantage in solar PV generation because the shifts in electricity production

are basically following the development of electricity demand. The PV modules are

most productive during times of peak in electricity demand when energy is at its

highest value (Baker et al. 2013). However, it is worth to mention that countries

geographically resembling Finland have opposite patterns of electricity consumption

in comparison to the cyclical movements of solar power. Diurnal and seasonal

variations are manageable with proper storage capacity and/or backup generating

sources which come into use when anticipated shifts in solar generation take place.

2.2.2 Intermittency

Intermittency arises when weather conditions exhibit short-term fluctuations that are

mainly caused by cloud covers. This directly reflects as a negative impact on

intra-hourly production of solar PV. Intermittency in solar power adds uncertainties

concerning the forecastability of electricity generation, which brings difficulties to

the power generation plan. To maintain system reliability under such circumstances,

additional system reserves and backup generation are needed on standby mode for a

quick response to the varying productions of solar PV, which results in growth of

system costs (Baker et al. 2013).

On small-scale systems the intermittency presents a big technical challenge in PV

generation. It can be somehow accommodated by geographically dispersed PV

generation on macro level. Short-term fluctuations in generation partially cancel each

other out across regions. Accordingly, the aggregation of short term PV generations

displays muted variation.

16

Because of the existence of variability and intermittency in solar PV generation,

improvements in grid management and storage technologies are essential for the

wide deployment of solar photovoltaics and further grid integration (Baker et al.

2013). In addition, the demand-side management can play an active role to ease the

tensions in energy markets, precisely by inducing consumers to adapt their

consuming behaviours to the supply of energy. Consuming energy when the supply

is high and avoiding consumption at times of undersupply. These acknowledged

solutions for addressing variability and intermittency lead us directly to the world of

smart grid.

17

3 SMART GRID AND PV

A smart grid is a vision of future electricity delivery system built upon the existing

power grid. It employs a variety of innovative solutions together with intelligent

monitoring, control, analysis and communication technologies for more efficient

operations in the whole electric power system (European technology platform for

electricity networks of the future 2015). The efficiency achieved at the system level

comes from its capability of management on both supply and demand side. Firstly, it

accommodates all generation and storage options to meet the timely varying

electricity demands of end-users. Secondly, it activates the demand response—a

mechanism by which end-users of different levels adjust consumptions in response to

changes in electricity price or other incentive payments. Lastly, it co-ordinates all

players in the energy market for an optimal outcome (IEA 2010b). The smart grids

are not one-day projects but a long process which once they are fully ready for use

are understood to be reliable, cohesively integrated, self-healing and resilient to

system anomalies, such as disturbances, attacks and natural disasters (Farhangi

2010).

The idea of building smart grids around the world is a response to the call for a more

energy efficient, more affordable, more sustainable and cleaner energy supply.

Behind the call we have aging electrical infrastructure, continuously growing and

timely varying demand for energy, the integration of intermittent renewable energy

sources and electric vehicles, unsecured electricity supplies and sizable GHG

emissions. All of them pose challenges to the global electric power systems and need

to be addressed in time. (IEA 2010b.)

Superiority of smart grid over the existing grid is explained by differences in system

structure. Deviating from the hierarchical structure, a smart grid has a network

structure which enables the interactions from both sides of the energy market through

advanced metering infrastructure while saving itself from domino-effect failures. See

Figure 4 and Figure 5. In a smart grid, electricity and market information flow in

both directions, from generation to transmission down to distribution levels and vice

versa (IEA 2011). This two-way digital communication between the utility and its

18

end-users fundamentally changes the way how energy is distributed and consumed in

the future.

Central

Generation

(Conventional and renewable energy sources)

Transmission System

Substations

Distribution Network

Customer Loads

(Industrial, commercial and residential)

Figure 4 The hierarchical structure of the existing grid

(Farhangi 2010).

19

Figure 5 The smart grid (Moxa Inc 2013, reproduced with permission).

Smart grids are essential for wide adoption of intermittent renewables. In particular,

the application of automation in control of generation and demand ensures balancing

of supply and demand. It thus facilitates the integration of intermittent renewable

energy sources (IEA 2010b). Smart grids more or less function as platforms to allow

renewable energy sources to compete effectively in a global environment. Without

them solar PV and other renewables are hindered from penetration due to increasing

integration costs. Growing trend of small-scale generation at or near consumption

place by consumers, often addressed as prosumers, further increases the need for

smart grids. Information exchanges in high volume, enabled by smart grids, are

required for such production method known as distributed generation. The future of

solar PV along with other renewables intertwines with the vision of smart grids. Only

a good foundation like smart grids can ensure a sustainable deployment of

intermittent renewable sources. After considering the technical feasibility and

challenges in the wide adoption of solar PV, the focus then shifts to the evaluation of

its economic value which lies in the core of deployment of solar photovoltaics.

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4 SHORT-RUN ECONOMIC QUESTIONS

To evaluate an underlying energy technology’s economic value, it is natural to start

by addressing short-run questions. In the short run, the prevailing PV technologies

don’t improve and neither does the existing electric power system to which it is

connected, thus both factors can be assumed constant. The evaluation of short-run

economic value is the evaluation of costs and benefits that accrue from an

incremental addition in PV capacity conditional on the state of existing power system

and prevailing PV technology (Baker et al. 2013).

4.1 Short-run costs

For the purpose of short-run costs’ measurement, a most commonly adopted

approach LCOE is applied here. In it levelized cost of electricity is used as a

benchmarking tool for comparing the costs of different electricity generation

technologies. It evaluates the unit cost of electricity in net present value for the

underlying technology over its lifespan. LCOE is often taken as a proxy for the

average unit price of electricity required to break even over lifespan of the

technology.

In addition, LCOE is useful when considering grid parity for emerging technologies

such as photovoltaics (Branker, Pathak and Pearce 2011). Grid parity describes the

situation when the lifetime electricity generation cost, i.e. LCOE, of an emerging

technology become competitive to the prices of electricity generated from

conventional sources on the grid. For calculation the prevailing electricity prices are

plugged into LCOE to obtain a range of the required solar PV system and financing

costs under grid parity. Commonly, grid parity is considered to be the prerequisite

for wide adoption of an emerging generation technology.

Regardless of the popularity of the LCOE in cost evaluation of different electricity

generation technologies, it has faced its own problems in applications. Criticisms

mainly focus on the accuracy of assumptions, missing justifications showing

understanding of the assumptions and low degree of completeness of LCOE (Branker

et al. 2011). Inaccuracies can easily lead to differing or contradictory results from the

21

same data. Branker et al. (2011) recommend sensitivity analysis and give

justifications in addition to assumptions made as accurately and realistically as

possible to account for uncertainty. Darling, You, Veselka and Velosa (2011)

propose the use of probability distributions for the input parameters of costs and

energy output, whose real values are unknown. Rather than a single value of LCOE,

this methodology produces a LCOE distribution which captures the cost uncertainty

of an energy project. Further improvements can be made in considering real

financing, technological and geographical variability in the LCOE (Branker et al.

2011).

The LCOE model applied below is originally proposed by Branker et al. (2011). A

more complicated version of LCOE is presented in the paper of Darling et al. (2011).

T

t t

tt

T

t t

tttt

T

t t

t

T

t t

tttt

r

dS

r

FMOI

r

E

r

FMOI

LCOE

0

0

0

0

)1(

)1(

)1(

)(

)1(

)1(

)(

, (1)

where tI = initial investment expenditures in dollars ($) in t = 0,

tO = operating costs in dollars in year t,

tM = maintenance costs in dollars in year t,

tF = interest expenditures in dollars in year t,

tS = rated energy output in kilowatt-hour (kWh) in year t,

d = system degradation rate in percentage,

tE = energy output in kWh in year t,

22

r = discount rate,

T = lifespan of the PV project.

The LCOE is expressed in a fraction with the costs on the top and the energy output

on the bottom, thus its value is in $/kWh. The net present value is obtained by using

discount factor. Most of the costs incurred over lifespan of the project can be traced

back to the initial investment expenditures including upfront costs and the financing

cost of the investment. Upfront costs come mainly from the cost of the solar PV

system. Note that the possible costs incurred by intermittency of solar PV are ignored

in the short-run cost analysis in that intermittency doesn’t impose significant costs

for small changes in solar PV penetration (Baker et al. 2013). The rest of the total

expense goes to operating, maintenance costs and interest payments if debt financing

was being used.

Normally a solar PV system needs quite a little maintenance compared to the

conventional power plants. However, the costs incurred by replacing inverters

periodically are not small enough to be ignored. The typical lifespan of an inverter is

in the range of 5 to 10 years compared to the 25-year warranty for a solar panel.

Consequently, the inverters can be replaced for two to three times during a solar

project. According to Branker et al. (2011), the replacement cost varied from 6% to

9% of total system cost for 2009 in US installations. Other cost factors that can be

considered for inclusion in the model are insurance, taxation and monetary incentives

from government.

The total energy output over the lifespan of a solar PV project consists of t years’

generation. The energy output in a given year equals the yearly rated energy output

tS after system degradation effects are taken into consideration. The straightforward

method to calculate the yearly rated energy output is to multiply the yearly operating

hours of the PV system, 8760 hours precisely, by the system size/capacity in kW and

the presumed capacity factor which is the ratio of actual energy generated to that by a

solar panel consistently exposed to sunlight at standard test conditions. Alternatively

with the help of a sophisticated meteorological database like Meteonorm or PVGIS,

23

the yearly local solar irradiation in kWh/m2 can be obtained and used for a more

accurate result. Instead of the system size, the surface area of a solar panel is

multiplied by the solar irradiation factor and the capacity factor. The system

degradation effects in the model are summed up with a predetermined rate d over

time. The degradation rate is generally assumed to be on the order of 0.5–1.0% per

year though the recorded rates for c-Si modules were lower (Branker et al. 2011).

As the metric suggests, an increase in any cost factor will result in an increase of

LCOE. The opposite argument applies to the rise of energy output level which

implies a higher capacity factor and/or a lower degradation rate. The change in

discount rate has a complicated effect on the LCOE. Branker et al. (2011) build an

example case of residential solar PV system with full debt financing and they provide

an interpretation of the effect as LCOE decreases with increasing discount rate

though to a limited degree. It is to be noted that the effect would be different if the

solar project is financed by equity (Zweibel, Mason and Fthenakis 2008).

The LCOE estimates of different PV technologies are reported to fall in the range of

$0.10–1.72/kWh with a predetermined discount rate of 3% which is normally the

reference rate for public projects. And the LCOE estimates vary from $0.29 to

$2.36/kWh with a discount rate of 15% for private investors. The lowest value of

0.10 is still higher than the typical LCOE estimates for natural gas or coal-fired

generation ranging from $0.07–$0.09/kWh. Based on the simple comparison, it

seems solar is not cost-competitive against the conventional generation technology in

the short run. (Baker et al. 2013.)

It is worth noting the application of LCOE alone is flawed for the evaluation of

economic value of a given generation technology despite of the wide application of it

in energy cost analysis. The intraday wholesale prices of electricity are very volatile

in the power market, varying in a wide range across hours, and thereby the economic

value of a unit of energy doesn’t remain the same. It rather depends on the market

condition when it is generated. (Joskow 2011.)

24

4.2 Short-run benefits

The short-run benefits that accrue from an incremental addition in solar PV capacity

should not be simply evaluated based on the quantity sold and the prevailing

electricity retail price as in the conventional way. To evaluate the benefits of solar

PV generation we can alternatively consider the cost cuts achieved by including extra

solar PV capacity in the power system compared to the generation supported fully by

conventional sources. The short-run costs are formed by variable costs from

operating and emission costs, so the consequent cost cuts should be evaluated in both

cost components. Following the short-run benefits model of Baker et al. (2013), we

present the value gained with an incremental increase in solar PV capacity in the

form of subtraction between total costs incurred without and with solar over a one

year time horizon.

,)()()()()(11

H

h

hhhh

H

h

hh KsyEMKsyCyEMyCKV (2)

where V = short-run economic value per year of installed solar capacity in $,

K = installed solar capacity in kW,

h = hour over one-year time horizon, Hh ,,1 ,

C = operating costs including fuel and other operating costs in $,

hy = load (electricity demand) in kW in hour h ,

= social cost of carbon in metric ton,

EM = total emissions in metric ton,

hs = solar PV output in hour h per unit of capacity (production factor).

25

The solar PV imposes quite little operating costs and generates electricity free of

emissions, which manifest as cost savings from lessened generation by dispatchable

energy sources. A solar generating unit is expected to run at its full capacity when

variable costs are close to zero, therefore the amount of on-grid solar dispatched is

assumed to be Ksh in the model. Baker et al. (2013) further assume hs is independent

of K , which is likely to hold for small changes in K . Another assumption concerns

the state of the power system which is assumed to be in its long-run equilibrium such

that the model accounts for only the operating margin. In the long-run equilibrium

the generation capacity built exactly meets the electricity demand, thereby no

additional capacity needs to be constructed and the change of energy output structure

has no impact on system capacity. Lastly, an increase in solar output is assumedly

accompanied by an equal amount of reduction in dispatchable generation ignoring

the possible differences in the transmission and line losses.

Differentiating equation (2) with respect to K gives

H

h

hhhhhh KsyEMsKsyCsKV1

)(')(')('

Denoting the marginal operating/economic cost hhh KsyC )(' and the marginal

emissions rate hhh KsyEM )(' gives

,)()('1

H

h

hhhh ssKV

(3)

The right-hand side of equation (3) can be alternatively expressed in another way by

substituting average values of all parameters for the marginal terms. Note that we

need to consider covariance here for the fact that there is positive correlation between

solar generation and electricity demand. In most areas solar generation is at its

highest level when the electricity demand peaks. Now introducing the concept of

population covariance together with the average values into the marginal value

function we obtain

26

)),,(()),(()(' sCovCFHsCovCFHKV

where and are average values over a year while capacity factor CF is the

respective average value of hs . The solar PV output covaries with marginal economic

cost and marginal emissions rate of dispatchable generating units in any given hour.

The sign of the covariance is positive for ),( sCov since both the marginal operating

cost and the solar productivity increase with the growth of demand. The sign of

),( sCov is, however, not straightforward to interpret. It is determined by the types

of the energy sources in use, power plant and its efficiency. The marginal emissions

rate can then vary in both directions as can the sign of ),( sCov .

System lambdas are often provided by local utilities when wholesale electricity

markets are regulated. Otherwise, the real-time locational marginal prices (LMPs)

can be applied to evaluate the generation by solar PV. The LMPs are

location-specific prices for supplying the next increment of electricity in the

least-cost manner given the bids/offers submitted by market participants and the

physical limits of the transmission system (Meeusen and Potter 2004). The LMPs

cover transmission congestion and line loss in addition to the marginal energy cost

captured by system lambdas, which justifies the preference of LMPs over system

lambdas in the evaluation of solar PV generation when the market functions without

any distortions (Baker et al. 2013).

The challenge of evaluating the marginal value of an increase in solar PV penetration

comes from the calculation of its marginal social value. We need to, first of all,

quantify the marginal environmental damages avoided by a new PV installation and

then monetize the damages. The environmental damages considered here are

primarily products of carbon dioxide emissions from power plants. The emissions

rates vary across energy sources from dirty coal to zero-emission renewable like

wind and solar. For this reason, the marginal emissions rate doesn’t stay constant but

varies with the fuel type of marginal generating units.

Furthermore, the location and time of day should be considered for capturing

marginal CO2 emissions as suggested by Graff Zivin, Kotchen & Mansur (2014).

27

They find that the heterogeneity of energy sources also causes wide spatial and

temporal variation in carbon dioxide emissions due to different electricity generation

plans in the United States. Regions often differ in the choice of main generating

sources, which explains the spatial fluctuations in emissions. The mapping of energy

mix to meet peak and off-peak demand results in varying emissions across hours,

low during on-peak hours and high during off-peak hours in the study of Graff Zivin

et al. (2014). This phenomenon is supported by the fact that natural gas electricity is

often used as backup source to meet peak demand in the US whilst coal is among the

most common baseload power sources. To account for the variations by location and

time of day, hourly emissions on the grid are regressed on hourly electricity

consumption to estimate the marginal emissions of electricity demand in the US.

(Graff Zivin et al. 2014.)

Callaway, Fowlie and Mccormick (2015) use a similar regression model to estimate

the marginal operating emissions rates. In their model the explanatory variable is the

electricity production at dispatchable fossil-fueled sources instead of electricity

demand. They take a step further to form clusters of daily observations in electricity

generation within a region and season that share similar generation profiles. The

clustering helps to identify the irrelevant variation in system-wide emissions resulted

from intra-daily fluctuations in generation dispatch and other systematic differences

in operating conditions. The variation left then better captures the effect of an

increment change of solar PV’s capacity on emissions.

The social value of a new installed PV capacity is the product of the social cost of

carbon and the carbon emissions avoided weighted by hourly solar PV generation.

The social cost of carbon (SCC) is defined as an estimate of the monetized damages

inflicted by an incremental increase in carbon dioxide emissions in a given year

(United States environmental protection agency 2015). It is normally available in a

range of values from governments for cost-benefit analyses.

4.3 Short-run net benefits

The short-run net benefits are the outcome of short-run benefits less short-run costs.

Insofar, the short-run net benefits of solar photovoltaics are universally reported to be

28

negative, which doesn’t promise a future for solar PV. The net cost is, for instance,

between $0.108 –$0.158 per kilowatt-hour when the displayed generation in question

is a combined-cycle gas-fired generation (Borenstein 2011), and it varies in a range

of $0.12–$0.31 per kilowatt-hour in the working paper of Baker et al. (2013).

However, we must keep in mind that the short-run net benefits depend, for a large

part, on the assigned value of social cost of carbon. The latest estimate of social cost

of carbon dioxide emissions given by Interagency Working Group (2015) is $36 per

metric ton of CO2 emissions for year 2015 in 2007 dollars assuming an average

discount rate of 3%. Despite of its official role in guiding the regulation of the

greenhouse gas emissions, this central value, included in the range of estimated

values from $11 to $105 per metric ton of CO2 emissions, is widely argued to be a

result of underestimation by omitting partially or wholly many of the biggest risks

associated with climate change such as wildfire damages (Howard 2014b). A more

thorough list of missing or poorly quantified damages associated with climate change

goes from conventionally recognized areas like health, agriculture and oceans et

cetera to productivity and economic growth, water, transportation, energy,

catastrophic impacts and being a tipping point in inter- and intra-regional conflicts

(Howard 2014a).

For the purpose of a simple numeric illustration of how different values of SCC can

dramatically affect the result, we conduct some calculations. The estimated SCC by

Moore and Diaz (2015) takes the value of $220 per metric ton of CO2 emissions

which is several times larger than $36. Substituting $220 for $21 used by Baker et al.

(2013) gives a new range of values. The net cost of an incremental addition in solar

PV capacity becomes now $0.009–$0.197 per kilowatt-hour which is almost

negligible on the lower bound. Conversely, we obtain the corresponding SCC values

to break even, i.e. roughly $237–$568 per metric ton of CO2 emissions. These

values, though unrealistically high compared to previous estimates, are well below

the largest value estimated by Ackerman and Stanton (2012) which is close to

$900/metric ton CO2 in 2010. According to Ackerman and Stanton (2012) the factors

driving this result are uncertainties related to the magnitude of climate changes, or

climate sensitivity. In light of their analysis we can conclude the short-run net value

29

of a new PV installation doesn’t need to be negative as had been conventionally

assumed.

30

5 LONG-RUN ECONOMIC QUESTIONS

In the long run, the PV technologies advance and the electric power system improves

over time. Therefore, the short-run constraints faced in solar PV generation are no

longer binding. More importantly, the cost imposed by intermittency of solar energy

starts to grow too big to be ignored in the assessment of solar’s economic value.

These intermittency-related costs are widely named as integration costs which arise

with the large-scale deployment of intermittent renewables in the power system. Our

starting point is to introduce the concept of the integration costs proposed by Hirth et

al. (2015). We then proceed to the long-run model developed by Gowrisankaran et

al. (2013). The model functions as a practical tool for the analysis of economic value

of solar PV in a long time horizon. However, it is noteworthy to mention that the

definition of long run in some papers, for instance that of Baker et al. (2013), differs

from that we use here. The medium run that Baker et al. use roughly corresponds

with the long run of this thesis while their long-run economic value intertwines with

the twenty-first century climate target.

5.1 Integration costs

5.1.1 Redefining integration costs

Integration costs are generally understood to be the costs incurred when the

renewables are integrated into the power systems. They are extra costs added upon

investment expenses, operating & maintenance costs and other LCOE components.

Following Hirth et al. (2015), we introduce the redefined integration costs in a simple

context of perfect and complete market.

Under the assumption of perfect and complete market, the marginal value of

intermittent renewable equals its market value. The market value is the revenue an

investor will receive by selling the electricity from the renewable in the electricity

market whilst excluding any governmental subsidies such as feed-in tariffs. To put it

in another way, the market value is simply the average electricity price weighted by

31

the share of renewable generation. Hirth et al. define the renewable-weighted average

electricity price with a summation operator as follows1:

T

t

N

n

nt

T

t

N

n

ntntsolar wpwP1 1 1

,,

1 1 1

,,,, .1such that ,

(4)

The solar-weighted average electricity price solarP here is the weighted sum of the

electricity prices at time t, location n and lead-time2, where the weights ,,ntw are the

shares of solar generation at time t, location n and lead-time τ. The physical

constraints of electricity in time, space and lead-time define that electricity is a

heterogeneous good (Hirth et al. 2016). For this reason, the price of electricity

doesn’t stay constant; it tends to vary over time, space and lead-time. Similarly, the

load-weighted average electricity price can be written as

T

t

N

n

nt

T

t

N

n

ntntyelectricit lplP1 1 1

,,

1 1 1

,,,, .1such that ,

The weights ,,ntl equal the shares of load at time t, location n and lead-time τ which

sum up to unity. Hirth et al. (2015) find that the market value of wind generation

declines with the degree of penetration, which is in concordance with the previous

studies’ finding (Lamont 2008, Joskow 2011). This can then be generalized to all

renewables as Hirth et al. notify in their paper. Applying this to our thesis, the loss in

the market value arises from the interaction between intermittency of solar PV and

the power system’s inflexibilities. Therefore, the integration costs of solar )(qsolar ,

equivalent to the loss in the market value of solar, can be defined as the spread

between load-weighted average electricity price and solar-weighted average

electricity price. Formally,

1 Note that we put solar as the subscript of price deviating from the originally used wind in the paper

of Hirth et al. (2015) and we do the same adaptions in the later parts of this thesis. 2 Lead-time is the amount of time that elapses between the electricity contract and delivery. Three

types of lead-times are applied in different markets: day-ahead market (12–36 hours before delivery),

intraday market (few hours before delivery) and balancing power market (real-time delivery). (Hirth,

Ueckerdt and Edenhofer 2016.)

32

).()()( qpqpq solaryelectricitsolar (5)

Equation (5) can be generalized to other generating technologies in addition to

renewables. If any deviation from the load-weighted average electricity price occurs,

the technology in question imposes integration costs. Hence, the definition of

integration costs is not restricted to variable renewables; instead it has its

applications in a broader range.

Note that all the components of equation (5) are functions of solar’s deployment

level q. The long-run optimal deployment q * of solar is given by the intersection of

marginal value and marginal costs of installing one increment of solar. In the perfect

and complete market the marginal value is equal to the market value which is

expressed as solarP . The marginal costs are LCOE of the solar energy as explained in

section 4.1. At the optimal deployment of solar, equation (5) can be written as

*).(*)(*)(*)(*)( qLCOEqpqpqpq solaryelectricitsolaryelectricitsolar (6)

The relationship between the market value of solar and its integration costs is borne

in the equation (6). Growing integration costs imply reduction in solar’s market value

and lessened deployment q*. In addition to the value perspective, Hirth et al. (2015)

propose a cost perspective to interpret equation (6). Rearranging equation (6) and

introducing the definition of system LCOE of solar to obtain

*).(*)(*)(*)( qsLCOEqLCOEqqp solarsolaryelectricit (7)

The system levelized cost of solar is the total economic costs of solar which consist

of two cost components: levelized cost of solar and the integration costs of solar. The

long-run optimality condition is realized when the equality between the average

load-weighted price of electricity and the system LCOE holds. In the long-run

optimum, the average load-weighted price of electricity is the same across the

market, which leads to the identical system LCOEs for generation technologies.

These two perspectives of evaluation of integration costs are summarized in Figure 6

33

given below. Integration costs are initially negative with small scale deployment of

solar, and they grow with the solar penetration. Negative integration costs are the

outcome of positive correlation between load and solar electricity generation. The

optimal deployment q* is defined by the solar LCOE and the market value of solar,

or equivalently by the average load-weighted price of electricity and the system

LCOE. When only considering grid parity for solar generation, we end up with the

sub-optimal outcome q0. Consequently, more than optimal amount of solar is

deployed, which results in deadweight loss represented by the shaded area.

q

q*

Integration costs =∆solar

Solar LCOE

Pelectricity

Psolar

Solar system LCOE

Integration costs = ∆solar

Grid parity

g

$/kWh

.

q0

Figure 6 Integration costs evaluated from two perspectives Hirth et al. (2015).

5.1.2 Decomposing integration costs

An efficient way to evaluate the integration costs of an energy source is to break

them down into small parts. Hirth et al. (2015) suggest the integration costs should

be decomposed into three approximately additive components according to

intermittent renewables’ three fundamental properties. Uncertainty, locational

heterogeneity and variability result in balancing costs, grid-related costs and profile

34

costs respectively. They are defined by Hirth et al. in terms of price or alternatively

of the market value of solar. We see all the three cost components as one source of

reduction in solar’s market value.

Balancing costs are the reduction in solar’s market value caused by deviations of

load from day-ahead generation schedules due to forecast errors. They represent the

marginal costs of balancing the deviations and are reflected as the spread between

day-ahead and real-time prices. Formally,

T

t

N

n

T

t

N

n

balancingsolar wlpwl

1 1 1 1 1 11

, 1such that ,)(

(8)

where p substitutes for ,,ntp in that only the lead-time information of the electricity

prices is set to be known for the calculation of lead-time specific costs. The same

argument applies to the load weights l and the generation weights w . Balancing

costs reduce to zero if the forecast errors of solar generation are perfectly correlated

to the forecast errors of load, which implies wl . When comparing specific

renewables, the solar forecast is argued to be more accurate than the wind forecast. If

the argument holds, solar generation will bear lower balancing costs.

The balancing costs of solar are estimated in a handful of papers with a specified

location, for example, a small-scale solar generation in California imposes balancing

costs of $1.7–$2.9/MWh (Luoma, Mathiesen and Kleissl 2014). Corresponding value

in Arizona is estimated to be on the order of $8/MWh at 30% penetration

(Gowrisankaran et al. 2013).

Grid-related costs are the reduction in solar’s market value caused by variations in

solar generations over locations in the power grid. They are quantified as the spread

between the load-weighted and the solar-weighted electricity price across all bidding

areas in the market. The grid-related costs imply varying marginal value of electricity

over locations and the presence of transmission constraints and line losses. Again,

grid-related costs can be expressed in a similar way as in equation (8).

35

T

t

N

n

T

t

N

n

nnnnn

N

n

relatedgridsolar wlpwl

1 1 1 1 1 11

. 1such that ,)(

The weights here take the subscript n denoting different locations. The assumption

here is that we know only about locations of the electricity prices but not the other

two variables time and lead-time. Solar PV, one of the most important technologies

for distributed generation, often produces electricity at the site of consumption.

Therefore the grid-related costs for solar can fall to a very low level.

Profile costs are the marginal costs of the temporal variability of solar generation

which leads to the reduction in the market value of solar. They reflect the marginal

value of electricity in different time period and the costs of storage and backup

generation to maintain the system reliability, i.e. to guarantee all-time exact match of

solar generation and load profiles. They are defined as the difference between the

load-weighted and the solar-weighted electricity price over time periods in a year.

T

t

N

n

T

t

N

n

ttttt

T

t

profilesolar wlpwl

1 1 1 1 1 11

. 1such that ,)(

The weights tl and tw are time-specific weights and they have the same value if solar

generation is perfectly correlated with load over time. The positive correlation

between solar power and the demand contributes to the relatively small size of

profile costs compared to other intermittent renewables and often negative profile

costs at low penetration rate. The literature review of cost estimations on solar PV

provides us a list of profile costs estimates which are in €/MWh. The profile costs are

negative across markets at low penetration (Borenstein 2008, Brown & Rowlands

2009, Mills 2011). They are in the range of 7–12 at the penetration rate of 10% and

3% in Arizona (Gowrisankaran et al. 2013).

Hirth et al. (2015) propose further decomposition of profile costs into two cost

components. One cost component is the costs that arise from output adjustment in

thermal plants, which is summed as flexibility effect. It accounts for scheduled

36

ramping and cycling3, and thus differs from the unexpected ramping and cycling in

balancing costs. A simulation based on German load and variable energy in-feed data

from 2010 is conducted to estimate the size of the flexibility effect by calibrating

penetration rate within the range of 0–40%. It shows residual ramps increase with

solar penetration. A 40% penetration rate results in 60% more cycles on average

power plants and the marginal cost of €3/MWh of renewables if €100/MW per cycle

is assumed. (Hirth et al. 2015.)

The utilization effect of profile costs imposes capital costs on thermal plants by

reducing its capacity utilization rate. Similarly, the capital costs of solar grow with

reduced utilization of solar. It is the case when the curtailments of solar happen at

times of negative residual load. The numerical estimation of the utilization effects

verifies the arguments given above. The utilization rate of thermal capacity is 70%

without any intermittent renewables and it drops to 47% as the penetration rate of

renewables grows to 40% at which level the utilization effect is estimated amount to

€51/MWh. (Hirth et al. 2015.) Even though the assumption of constant capital costs

for thermal plants is unrealistic and overly simplifying, the result it gives is good

enough to quantify the utilization effect. Hirth et al. believe the mitigation brought by

adjustments on the thermal capacity is considerably small so that the findings remain

valid.

Aggregating the calculated values of balancing costs, grid-related costs and profile

costs we can obtain a value for integration costs of a particular renewable technology

at a particular rate of deployment. The value is, however, not unbiased. Hirth et al.

(2015) note that integration costs also consist of a residual term which depicts the

interactions between all three cost components. However, the size and direction of

the interactions are unknown and further analysis should be done. Thus a full

coverage of all the cost components of integration costs and LCOE should be given

to evaluate the long-run economic costs of intermittent renewable sources.

3 Ramping is the change in power flow (or power generation) from one time unit to the next (Nord

Pool Spot 2015). Cycling is the combined effects of increased start-ups, ramping and periods of

operation at low load levels on thermal units (Troy, Denny and O’Malley 2010). However, the term

“cycling” used by Hirth et al. (2015) has a limited meaning concerning ramping only. It is measured

in terms of system cycles and is the sum of upward residual load ramps over peak load during a year,

where the residual load is load net of intermittent renewable generation.

37

5.2 The model of Gowrisankaran et al. (2013)

The approach of integration costs captures the different aspects of intermittency that

impose costs and reduce market value of renewables. It clarifies the three sources of

integration costs through the decomposition of costs. Another way to evaluate the

social costs of renewable energy is to set welfare-maximizing problems from the

perspective of a system operator and obtain the values of social costs by solving for

the decisions that maximize total surplus at different deployment levels of a

renewable (Gowrisankaran et al. 2013).

The model developed by Gowrisankaran et al. (2013) is a revised version of the

model of Joskow and Tirole (2007), who present an expected-welfare-maximizing

problem of a system operator faced with fossil fuel generators that can fail at any

time. In the model of Gowrisankaran et al., the intermittency of renewable energy is

taken as one source of unexpected generator failures and different parameters are

considered for a realistic and relatively simple application with available data from

southeastern Arizona. Most importantly, their model reoptimizes operator decisions

as a function of renewable energy penetration. Accordingly, the system operator

balances between the welfare loss of consumer from power outage and demand-side

management and the cost imposed by maintaining and running extra capacity for an

optimal decision.

5.2.1 The model setting

The model has a two-stage setting. In stage one, the system operator makes two

decisions. One decision is made on whether and how much to invest on capacity by

building new generating units. The other decision is to set the price for interruptible

power contracts4 and offer them to the customers. In stage two, the system operator

has on her hand the weather forecast made a day before and a list of fossil fuel

generators which are scheduled for maintenance. She then makes her own forecast of

4 The interruptible power contract is a contract made between a consumer and the system operator to

agree on power curtailment of the consumer against monetary compensation in the event of power

outage.

38

solar generation and load, based on which she can draft the lists of fossil fuel

generators scheduled for production and operating reserves respectively and decide

how much load to curtail from the group of customers who have signed up for

interruptible power contracts. These generation scheduling and demand-side

management decisions are assumed to be made in discrete time horizons, i.e. each

hour of each year over the lifespan of generators. Ramping and startup costs are

dropped out of the model for the sake of simplicity.

There are two possible outcomes after the realization of load and generation. If the

load is more than the generation and operating reserves after adjusting for line losses,

a power outage occurs and a random set of customers are cut off from the power

supply. Overloading, negative forecast error of solar generation and unexpected

fossil fuel generator failure can, any of them individually or jointly, cause the power

outage. Conversely, when the load is less than the generation and operating reserves

after adjusting for line losses, the operator will adjust down the rate of generation for

one or more generators to balance supply with demand.

5.2.2 The stage-two optimization problem

The model contains two optimization problems which are solved backwards.

Gowrisankaran et al. (2013) assume the first-stage decisions to be optimal, so the

second-stage welfare-maximizing problem is the first one to be addressed. The

variables, with respect to which the welfare is maximized, concern the decisions of

generator scheduling no

and the amount of demand needed for curtailment z. The

consumer benefits are determined jointly by the status of power outage outage, the

expected outage hours times fraction of customers without power in the event of

power outage doutage, and the total load value net of consumers’ welfare loss from

curtailment QD*VOLL – WLC. The definition of the parameters is given below.

Firstly, the parameter outage features the status of power outage and it takes the

value 0 or 1.

39

,)()(1),,(1

FFnJ

j

SLSLSLjj SndzpDLLzpDSnonxwznooutage

where no

= generator scheduling indicator of 0–1 (0 for off and 1 for on),

z = amount of demand needed for curtailment,

w

= weather forecast including forecast of cloud cover, temperature,

the time of day, day of week and time after sunrise and sunset etc.

j = index for existing fossil fuel generators, j = 1,…, J,

nFF= number of new fossil fuel generating units,

nSL = number of solar generating units, equivalently solar capacity,

SnSL = solar generation, where ),|(.~ wFS s

following a state-

contingent distribution,

dSL = fraction of distributed solar out of the solar capacity.

The arrow above the parameters indicates the randomness. )( jj onx is specified as

the maximum output by generating unit j and formed as

otherwise. ,0

)1( prob. with ,

)(

jFailjj

ji

onPk

onx

When put on, each generating unit has a probability of failure FailjP in any period.

The failure occurrences are assumed to be independent and identically distributed.

40

The demand function of electricity is assumed to have a constant price elasticity for

prices no more than a reservation value v. Specifically the retail price of electricity is

assumed to be constant at p per megawatt-hour (MWh). The scale D follows a

state-contingent distribution which has a lower bound ).(min wD

The general form of

the demand function is

. ,

,0

),(

vppD

v p

DpQ D

The line losses expression in the function of outage is based on Bohn, Caramanis and

Schweppe (1984) and Borenstein (2008) assuming line losses in any period to be the

product of a parameter α and the square of non-distributed generation. Formally,

,)( 2LLQLL where Q = load net of demand curtailment and distributed solar

generation. Solving the equation the operator obtains line losses as a function of Q,

which is )4121()2()( 1 QQQLL . The derivative of LL with respect to

Q is QdQdLL 4121 . The growing share of distributed solar in

generation reduces the value of Q, which in turn reduces the line losses. This is most

pronounced when distributed solar generation occurs at peak load periods, in other

words, when Q has a high value. Q can be written in a more inclusive manner

as SndzpD SLSL .

Back to the outage indicator presented in the previous page, the interpretation of it is

straightforward, power outage occurs when the maximum realized fossil fuel and

solar generation is below the level of load plus line losses net of curtailed demand.

The value of lost load (VOLL), also known as the value of unserved energy,

measures the opportunity cost of outages from the perspective of consumers. It

functions as a proxy for the wholesale electricity price among other variables.

(Willis & Garrod 1997.) With the demand function ),( DpQD and the retail price of

electricity at p , VOLL takes the form as a fraction of the area under the demand

curve over the entire demand schedule.

41

Formally,

.1

)(1

)(1

),(

),(),(

1

11

11

pnpv

pD

pnvD

pD

pDppvD

pD

pDpdppD

DpQ

DpQpdpDpQVOLL

v

p

D

Dv

p

D

The welfare loss from curtailment in any stage-two period is a function of the

amount of demand needed for curtailment z and the price of interruptible power

contract pc. The interruptible power contract provides to consumers a monetary

compensation of ppc for every unit of electricity foregone to exchange for the

flexibility on demand-side management. In each stage-two period, the system

operator chooses the amount of demand needed to be curtailed z and randomly

selects customers for curtailment from the list of contracted, who happen to use

electricity in the underlying moment. However, if it is possible for the operator to

curtail demand in the ascending order of load valuation by end-users, it will lead to

more efficient rationing and higher level of total welfare level (Gowrisankaran et al.

2013). Let ),( DqP denote the inverse demand curve, solving for P in terms of q and

D the operator obtains .)( 1qDP The welfare loss from curtailment then has a

form of

.))(1(

)(

)(11)(

)(

),(),(),(

),(

11

11

1

),(

),(

1

),(

),(

c

c

c

c

DpDQ

DcpDQ

c

DpDQ

DcpDQ

cDDc

pp

ppz

pDpDD

ppD

z

dqqDpDpD

z

dqDqPDpQDpQ

zpzWLC

42

Now the consumer benefits are expressed

as mwpzWLCVOLLpDwznooutagedE coutage

,|)),())(,,(1( . They are the

expected sum of total load value net of consumers’ welfare loss from curtailment

conditional on the two random variables, weather forecast w

and maintenance status

of existing fossil fuel generators m

. The maintenance status is an indicator variable

with value 1 denoting the status of being under maintenance, thus unavailable for

production and conversely value 0 denoting the availability of generators. The

maintenance status indicator is the exact opposite of generator scheduling

indicator no

such that .01 jj onm

The generation costs are ex post minimized costs of generation and reserves. They

are a function of residual load and line losses net of curtailment, and realized

generation .x

The generation costs are formed

as mwnoxQQLLSnzpDPCE SL ,|))()),4121()2((( 1 .

Combing the benefits and costs the operator obtains the stage-two optimization

problem. Formally,

.01such that

,|))()),4121()2((

(

)),())(,,(1(

max),|,(

1

,

jj

SL

coutage

znocFF

onm

mwnoxQQLL

SnzpDPC

pzWLCVOLLpDwznooutaged

EpnmwW

5.2.3 The stage-one optimization problem

The stage-two optimization problems are solved for all hours of a year. With the

hourly expected values known, the operator can go back to the first stage. She needs

to choose the investment level and price for the interruptible power contract. The

decisions can be made simultaneously or sequentially depending on how the stage-

one optimization problem is set. If the operator wants to solve for the optimal values

one at a time, she can take one variable as given and solve for the other one.

43

Given the investment level of fossil fuel generators, the system operator sets the

price for the interruptible power contract to maximize expected welfare for a year.

),|,(max)( cFFc

p

FF pnmwWHEnV

,

where H equals the number of hours in a year. Lastly, the operator plugs the optimal

value of pc into the value function of expected total surplus for a year, and obtains

the optimal level of investment.

)},()({max* SLFFFFSLSLFFFFn

nTFCFCnFCnnVV

where FCSL and FCFF are investment costs of solar, or fixed costs of solar per MW of

capacity, and investment costs of fossil fuel respectively. The present value of

equipment investment and maintenance costs is marked as TFC which is the AFCT,

practically average transmission fixed cost per MW, times the maximum expected

load net of distributed solar.

}.)()({max)( wSndpwDEAFCnTFC SLSLw

TSL

The increased penetration of distributed solar results in reduction in fixed costs of

transmission. Note that the expected annual total surplus changes with the solar

penetration rate nSL.

5.2.4 Summary of the findings from Gowrisankaran et al. (2013)

Gowrisankaran et al. (2013) use the model to evaluate the economic value of solar

PV deployment in southeastern Arizona. Their estimated social costs excluding the

carbon benefits fluctuate in a range of $126.7–$138.4 per MWh. The social costs

reach its highest value at the penetration rate of 20% of which intermittency accounts

for $45.9 and unforecastable intermittency for $6.1. Thus the unforecastable part of

intermittency doesn’t really impose such big costs as generally believed. The initial

investment expenses, or solar panel costs, on the contrary, contribute most to the

44

total costs of solar generation. To specify, the median installed price of residential

and commercial PV system in US for year 2012 ranges from $3.2–$6.1 per Wdc

(Barbose 2014: 54–63). Based on the calculation of Gowrisankaran et al. (2013), the

price of solar system needs to drop to $1.48/W for 20% penetration to be welfare

neutral with a social cost of carbon set at $36 per metric ton of CO2 emissions. As we

have mentioned in section 4.3, the social cost of carbon presently in use is argued to

bias downwards by a large margin. If we assign a large value to it to justify taking

actions to slow down climate change, the installed price of solar at present level can

be cost-effective.

As pointed out by Gowrisankaran et al. (2013), their model has its limitations such

that optimizations are not done in a dynamic manner between periods. The exercise

of market power is not considered in the model while it is generally known the

electricity distribution utilities are natural monopolies. Ignoring this fact can lead to

divorce from the reality and poor applicability of the model. Furthermore, the values

of operating reserve costs come from approximation.

45

6 CASE STUDIES ON SOLAR PV DEPLOYMENT

In this thesis particular emphasis is placed on the solar generation potential in

Finland. Previous chapters have built an understanding of the solar market from a

technical perspective. We are also equipped with tools for better evaluation of solar

generation from the point of view of both economy and whole society.

Next, we present the cases of solar deployment in two countries. Firstly, we review

the German solar PV market. Germany is the leading country in the world in

adopting solar PV and its total installed PV capacity has reached to 38.9 GW by the

end of June 2015 (RECAI 2015). We are interested in comparing its weather

conditions for solar generation with that of Finland since Germany has been

commonly used as reference country for the potential of solar generation in Finland.

It is often argued that the weather conditions for solar PV production in Finland are

as good as those in Germany. According to Šúri, Huld, Dunlop and Ossenbrink

(2007), the climate conditions are found comparable between northern Germany and

southern Finland. This finding has then been extensively reported in Finland.

However as both countries are relatively large, a misunderstanding possibly arises

from matching up the weather conditions between the two countries in a general

sense.

Secondly, we briefly introduce the current situation of solar deployment in Finland

and proceed to estimate the annual solar irradiations for a dozen of Finnish cities by

using meteorological database named meteonorm. The annual solar electricity yield

is calculated with MATLAB accounting for the energy losses from DC/AC

conversion. We also present several European cities’ annual solar electricity yield for

the purpose of comparison.

6.1 PV deployment in Germany

Germany has the most developed solar PV market in the world. It still claims the

world’s first place in total installed capacity of solar photovoltaics even though it has

gone through a slowdown lasting for four consecutive years since year 2010 (RECAI

46

2015). In 2014 Germany’s new installations were the second most in Europe with 1.9

GW.

In 2014 Germany, like Italy and Greece, could cover more than 7% of its electricity

needs with solar power (SolarPower Europe 2015). Its PV sector employed around

60 000 people in 2013 (IEA PVPS 2014). All these achievements can be attributed

to the government policies favouring renewable energy sources. The amicable

political environment surrounding renewables has directly led to a prosperous solar

PV market despite of the fact that the weather conditions in Germany for solar

generation are comparatively unfavourable.

The development of solar photovoltaics deployment in Germany has closely

followed the development of related support policies. The landmark in the policy

framework surrounding renewables was established in 1990, when the term Feed-in

tariff (FiT) was introduced for the first time. Feed-in tariffs are a policy mechanism

designed to promote the renewables deployment by paying the producers a

predetermined fee, higher than the retail electricity rate, for the electricity produced

and injected into the